This invention relates broadly and generally to a modular construction block, vertical wall or other structure constructed of an assembly of such blocks, and method for constructing a vertical wall or other structure. Such structures are commonly formed of hollow masonry units with cores filled with loose material and/or grout. This construction method generally provides reduced wall thickness, while allowing insulation and reinforcement to be included in the cores to increase thermal and structural performance. In an exemplary embodiment, the present disclosure comprises a molded and integrally formed masonry construction block. The block may be made from Portland cement, coarse and fine aggregates, water and various admixtures. In alternative embodiments, the exemplary construction block may be formed in parts, and may be constructed of other suitable natural or synthetic materials.